Chemical kinetic considerations

From experimental results and chemical kinetics considerations, the function P0 = f(t) may be established, and the lifetime, tF, determined by... 

The problems of parametric estimation and model identification are among the most frequently encountered in experimental sciences and, thus, in chemical kinetics. Considerations about the statistical analysis of experimental results may be found in books on chemical kinetics and chemical reaction engineering [1—31], numerical methods [129—131, 133, 138], and pure and applied statistics [32, 33, 90, 91, 195—202]. The books by Kendall and Stuart [197] constitute a comprehensive treatise. A series of papers by Anderson [203] is of interest as an introductory survey to statistical methods in chemical engineering. Himmelblau et al. [204] have reviewed the methods for estimating the coefficients of ordinary differential equations which are linear in the... 

The processes involved in the low pressure synthesis of diamond are not yet clearly understood, but various models have been proposed on the basis of thermodynamic and / or chemical kinetic considerations and a number of in situ as well as ex situ diagnostic studies. Figure 3 is a schematic representation of the diamond deposition process as it is understood today. 

Chemical kinetic considerations are another criterion. For example, a model can be eliminated if it requires the precipitation of a mineral that is known not to precipitate readily in low temperature systems. 

The species production rate r-must be obtained from chemical kinetics considerations and is dependent on the local thermodynamic state and the stoichiometric coefficients associated with the chemical reactions. 

From chemical kinetic considerations, it follows that the rate of production of A by the unimolecular reaction 5 is of the form... 

Representative Method Although each chemical kinetic method has its own unique considerations, the determination of creatinine in urine based on the kinetics of its reaction with picrate provides an instructive example of a typical procedure. 

As described in the first part of this chapter, chemical thermodynamics can be used to predict whether a reaction will proceed spontaneously. However, thermodynamics does not provide any insight into how fast this reaction will proceed. This is an important consideration since time scales for spontaneous reactions can vary from nanoseconds to years. Chemical kinetics provides information on reaction rates that thermodynamics cannot. Used in concert, thermodynamics and kinetics can provide valuable insight into the chemical reactions involved in global biogeochemical cycles. 

The field of chemical reaction engineering (CRE) is intimately and uniquely connected with the design and scale-up of chemical reacting systems. To achieve the latter, two essential elements must be combined. First, a detailed knowledge of the possible chemical transformations that can occur in the system is required. This information is represented in the form of chemical kinetic schemes, kinetic rate parameters, and thermodynamic databases. In recent years, considerable progress has been made in this area using computational chemistry and carefully... 

In this introductory chapter, we first consider what chemical kinetics and chemical reaction engineering (CRE) are about, and how they are interrelated. We then introduce some important aspects of kinetics and CRE, including the involvement of chemical stoichiometry, thermodynamics and equilibrium, and various other rate processes. Since the rate of reaction is of primary importance, we must pay attention to how it is defined, measured, and represented, and to the parameters that affect it. We also introduce some of the main considerations in reactor design, and parameters affecting reactor performance. These considerations lead to a plan of treatment for the following chapters. 

The process control of the post-exposure bake that is required for chemically amplified resist systems deserves special attention. Several considerations are apparent from the previous fundamental discussion. In addition for the need to understand the chemical reactions and kinetics of each step, it is important to account for the diffusion of the acid. Not only is the reaction rate of the acid-induced deprotection controlled by temperature but so is the diffusion distance and rate of diffusion of acid. An understanding of the chemistry and chemical kinetics leads one to predict that several process parameters associated with the PEB will need to be optimized if these materials are to be used in a submicron lithographic process. Specific important process parameters include ... 

Technically, there is no reason to limit consideration to homogeneous flows. However, since the micromixing time and location-conditioned expected values will be independent of particle position, we do so here in order to simplify the notation and to isolate the problems associated with the chemical kinetics. 

Historically, some of those approaches have been developed with a considerable degree of independence, leading to a proliferation of thermochemical concepts and conventions that may be difficult to grasp. Moreover, the past decades have witnessed the development of new experimental methods, in solution and in the gas phase, that have allowed the thermochemical study of neutral and ionic molecular species not amenable to the classic calorimetric and noncalorimetric techniques. Thus, even the expert reader (e.g., someone who works on thermochemistry or chemical kinetics) is often challenged by the variety of new and sophisticated methods that have enriched the literature. For example, it is not uncommon for a calorimetrist to have no idea about the reliability of mass spectrometry data quoted from a paper many gas-phase kineticists ignore the impact that photoacoustic calorimetry results may have in their own field most experimentalists are notoriously unaware of the importance of computational chemistry computational chemists often compare their results with less reliable experimental values and the consistency of thermochemical data is a frequently ignored issue and responsible for many inaccuracies in literature values. 

In the case of heterogeneous surface burning of a particle, consideration must be given to the question of whether diffusion rates or surface kinetic reaction rates are controlling the overall burning rate of the material. In many cases, it cannot be assumed that the surface oxidation kinetic rate is fast compared to the rate of diffusion of oxygen to the surface. The surface temperature determines the rate of oxidation and this temperature is not always known a priori. Thus, in surface combustion the assumption that chemical kinetic rates are much faster than diffusion rates cannot be made. 

Various ceramic membranes, for example, possess differing degrees of acid/base resistance, depending on the pH value, particular phase of the membrane material, porosity, contact time and temperature. However, no quantitative data are available on the kinetics of chemical dissolution of ceramic membranes as a guide for chemical corrosion considerations. 

Our ability to develop detailed chemical kinetic models has improved considerably over the past decade because of simultaneous developments in a... 

The philosophy used to develop detailed chemical kinetic mechanisms for gas-phase reactions can, in principle, be extended to treat heterogeneous reactions, provided diffusion is also considered in the final analysis. Clearly, the problem in heterogeneous catalysis is considerably more complex because of the close proximity of a large number of atoms and their collective effect on reaction kinetics and mechanisms, and the inevitable variation of catalyst structure with time—for example, as a result of sintering and poisoning. 

In siunmary, although the application of detailed chemical kinetic modeling to heterogeneous reactions is possible, the effort needed is considerably more involved than in the gas-phase reactions. The thermochemistry of surfaces, clusters, and adsorbed species can be determined in a manner analogous to those associated with the gas-phase species. Similarly, rate parameters of heterogeneous elementary reactions can be estimated, via the application of the transition state theory, by determining the thermochemistry of saddle points on potential energy surfaces. 

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